pre cal drill

Developed by Susan Canteyand student Elizabeth Albert

at Walnut Hills H.S.2006

Welcome to the

Pre-Calculus Power Point Flash Drill!

I’m going to ask you a lot of questions about math. These are facts that you should know extremely

well. You also need to be able to recall them quickly if you want to succeed in Calculus.

When you think you know the answer,

(or if you give up ) click to get to the next slide to see if you were correct.

Ready?

Define an

Even Function

)()( xfxf

Note: It is NOT enough to know the graph is

symmetric with respect to the y-axis.

Define an

Odd Function

)()( xfxf Again, please note that it is NOT enough to know that the graph has origin

symmetry.

See if you can identify the function that probably goes with each of these simple

graphs….

lyrespective

xxf

and

xxf

)(

)( 2

How about these?

lyrespective

xxf

and

xxf

3

3

)(

)(

What about this one?

2

2

xxf 1tan)(

Did you know it?

You are a tiger!

How about these?

xxf

1)(

and222 ryx

respectively

and finally:

lyrespective

xxf

and

exf x

ln)(

)(

The graph of x = a

is…

… a vertical line.

The graph of y = a

is…

… a horizontal line.

OK…that’s enough about graphs!

Let’s move on…

?1 x

x

1

?2/1 x

x

?2 x

2

1

x

?n mx

nm

xThink “flower” & “root”

?ln nx

xn ln

?ln xy

yx lnln

?ln y

x

yx lnln

?

?log xb

b

x

ln

ln

?1

ln

x

xln

?1ln

0

?ln xe

x

?ln xe

x

OK…enough of the logs already!

The formula for the slope of a

line is

m = ?

12

12

xx

yy

x

y

Point slope equation of a

line ?

)( 11 xxmyy

Midpoint Formula = ?

2,

22121 yyxx

Distance Formula=?

212

212 )()( xxyy

xDefine:

{|x|x for x 0-x for x<0

?98.2

2(Greatest integer < 2.98)

?17.2

3You always round

down the number line!

Here comes your favorite thing!

Yeah! Trigonometry!

?0sin

0

?0cos

1

?6

sin

2

1

?4

sin

2

2

2

1or

?3

sin

2

3

?2

sin

1

?2

cos

0

?3

cos

2

1

?4

cos

2

2

2

1or

?6

cos

2

3

?cos

1

?0tan

0

?4

tan

14

sin4

cos

because:

?2

tan

(or undefined)

?3

tan

3

?6

tan

3

1or

3

3

What are the Principle domains of the 6 trig

functions?

That is, what quadrants are the angles in which can be used to

answer inverse trig function problems?

2,2

2,2

,0

for cosine

for sine

for tangent

(Different texts assign different principle domains to the other three trig functions,

so we won’t bother with them.)

?2

1sin 1

6

?2

1cos 1

4

3

?2

3sin 1

3

?1tan 1

sine and cosine have to be equal!

4

?3tan 1

3131

0

31

13

Answer:3

OK…now let’s see if you know your identities!

?cossin 22 xx

1I hope you knew that one!!!

?sin 2 x

x2cos1OK, that’s really the same one!

?sin 2 xWhat’s the one with the ½’s in it?

x2cos21

21

That one is harder, but you will need it in calculus!

?cos2 xDo you know both of them?

x

and

x

2cos

sin1

21

21

2

You rock!!!

?tan1 2 x

x2secDid ya get the ol’

“stamp of approval” on that one?

?1sec2 x

x2tanThey’re laughing because this is really the same

one again!

?sincos 22 xx

Ho Ho Ho!!

x2cosI don’t know why Santa thought

this was funny!

?2sin x

xx cossin2This one is very important!!

Now for a little algebra and you’ll be done!!

?22 ba

baba

?33 ba

22 bababa

Notice there is NO “2”

?33 ba

22 bababa Still no 2!!!

?)( 2 ba

(almost finished!!!)

22 2 baba There’s that two you wanted before!!

Last one!!!!

3ba

3223 33 babbaa Don’t be foiled!

Use the binomial

Theorem.

If you know all this material, then you are prepared to begin

calculus… All you need now is a sharp mind, a sharp pencil and

a really big eraser!

GOODBYE!!!!

ADIOS!

AUFWIEDESEHEN!

CHOW!